Vol. 7, No. 11

November 2005

PQ Systems

Visit QualityAdvisor.com for statistical answers

Quality Quiz: With a video!

Six Sigma

Data in everyday life

Bytes and pieces

FYI: Current releases


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Quality Quiz from Professor Cleary

"B" is the correct answer!

Click here for a more complete video explanation.

Marsha's luck has run out, and the number 7 has not been her friend in this case.

To understand the rule of 7, it is useful to illustrate with a coin-toss example. What is the probability of getting a “heads” by flipping a coin? The answer, as any student will attest, is 50%.

The chance of getting two "heads" with two coin tosses diminishes to 25%.

The following figure demonstrates this probability graphically:

This is called a probability tree, with four possible outcomes: HH, HT, TH, or TT. One way to respond to the question about the probability of two heads in a row with two flips of the coin is to say that it represents one possibility in four potential outcomes, or a one in four (25%) chance.

A second way to look at the question is to introduce the probability multiplication rule

P(A and B) = P(A) x P(B)

The probability of event A and B occurring is equal to the probability of event A taking place times the probability of event B taking place. In this case, event A is tossing a “heads” (.5), and event B is getting “heads” again.

P(heads and heads) = P(heads) x P(heads)

= .5 x .5

= .25

Introducing the concept of a control chart and asking about the probability of seeing an above the process average (), one can see that it would be 50% for a process that is in control. The same would be true for the probability of getting an below the process average ().

So the probability of two s above the process average (or ) in a row can be illustrated with a sample space like the coin flip, except that instead of "heads" and "tails," it reprsents above or below the process average ().

Therefore, the probability of getting two s in a row above the process average () is .25.

The next question might relate to the probability of seven s in a row above the process average:

A = above, B = below

The likelihood of getting seven s in a row above the process average when the process is in control is .0078

We still haven’t answered the question, “Why 7?” One answer is that when Ford Motor Company began utilizing SPC in process improvement, the company’s SPC manual designated 7. In manufacturing settings, this became somewhat of an industry standard. Statisticians Duncan and Hughes subscribe to 7, while AT&T and Western Electric insist on 8.

SQCpack or CHARTrunner users don’t have to worry about any of this, of course, since the software has built-in rules about 7 points above or below the process average. A user can change the out-of-control rules, either creating customized rules or selecting from more than 15 of the most commonly-used out-of-control tests. There are a number of out-of-control tests that are especially appropriate for healthcare applications, for example.

Click here to register for the free Quality Gamebox program.

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